It is first pointed out by Henrick et al. in [1]},
that the desired convergence rate of the fifth-order WENO-JS was not
achieved for many problems where the first and third derivatives of
the flux do not simultaneously vanish and the behavior of the scheme
is sensitive to \(\epsilon ,\)  a parameter is introduced in order to
avoid division by zero in the evaluation of non-linear weights. They
suggested an improved version of the WENO-JS scheme which is termed
as mapped WENO and abbreviated by WENO-M. By using a mapping function
on the nonlinear weights, WENO-M satisfies the sufficient condition
where WENO-JS fails and obtains an optimal order of convergence near
simple smooth extrema. Consequently, higher order WENO schemes were
developed based on mapping function in [2]}.
